login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A330652 Decimal expansion of (phi^phi - 1/phi)/2. 0
7, 8, 0, 2, 1, 1, 7, 8, 9, 5, 9, 3, 8, 5, 2, 1, 4, 9, 5, 8, 3, 9, 7, 9, 4, 3, 4, 2, 5, 2, 8, 0, 3, 8, 6, 7, 0, 4, 3, 3, 6, 7, 0, 6, 0, 9, 4, 3, 7, 4, 5, 8, 7, 4, 6, 0, 6, 1, 6, 6, 6, 5, 0, 6, 7, 1, 0, 8, 9, 9, 9, 3, 3, 5, 6, 9, 6, 1, 8, 7, 6, 1, 9, 9, 9, 0, 4, 7, 7, 8, 5, 0, 4, 1, 3, 9, 7, 2, 5, 0, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: (phi^phi - 1/phi)/2 = integral from 0 to infinity of the function e^(-x*(2 + phi))*(cosh(x) + sqrt(5)*sinh(x))^phi, where phi = (sqrt(5) + 1)/2  (A001622).

LINKS

Table of n, a(n) for n=1..101.

Alexander R. Povolotsky, Interesting Integral, post in newsgroup sci.math.research, April 04, 2017.

EXAMPLE

.78021178959385214958397943425280386704336706094374587460616665067108999335696...

MATHEMATICA

RealDigits[(GoldenRatio^GoldenRatio - 1/GoldenRatio)/2, 10, 120][[1]]

PROG

(MAGMA) (((Sqrt(5)+1)/2)^((Sqrt(5)+1)/2) - 1/((Sqrt(5)+1)/2))/2

CROSSREFS

Cf. A001622 (golden ratio phi).

Sequence in context: A221114 A198841 A332634 * A181438 A333972 A088396

Adjacent sequences:  A330649 A330650 A330651 * A330653 A330654 A330655

KEYWORD

nonn

AUTHOR

Vincenzo Librandi, Dec 29 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 24 15:05 EDT 2021. Contains 346273 sequences. (Running on oeis4.)